Problem: $\overline{AB}$ = $\sqrt{130}$ $\overline{BC} = {?}$ $A$ $C$ $B$ $\sqrt{130}$ $?$ $ \sin( \angle BAC ) = \frac{7\sqrt{130} }{130}, \cos( \angle BAC ) = \frac{9\sqrt{130} }{130}, \tan( \angle BAC ) = \dfrac{7}{9}$
Answer: $\overline{AB}$ is the hypotenuse $\overline{BC}$ is opposite to $\angle BAC$ SOH CAH TOA We know the hypotenuse and need to solve for the opposite side so we can use the sine function (SOH) $ \sin( \angle BAC ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\overline{BC}}{\overline{AB}}= \frac{\overline{BC}}{\sqrt{130}} $ $ \overline{BC}=\sqrt{130} \cdot \sin( \angle BAC ) = \sqrt{130} \cdot \frac{7\sqrt{130} }{130} = 7$